1. Field of the Invention
The present invention relates to a robot apparatus that arbitrarily tilts an axis of an ellipse, indicating a stiffness characteristic, at a tip of a link.
2. Description of the Related Art
In a control method of a manipulator, it is important that an end effector (e.g., a hand) provided at a tip of a link can softly touch a subject. The application of this concept to an industrial robot can realize a collaborative work of a robot apparatus and a person. An operation of fitting parts can be facilitated by controlling a direction of flexibility of a hand. The application of this concept to a legged mobile robot can ease a shock to a body, since the robot can softly land on a surface to absorb bumps, whereby the robot can stably walk on an irregular ground.
In order to realize a control for flexibility of a hand, an impedance control in which a force sensor is mounted to a hand, or a control with an artificial muscle actuator has been executed. It has been known that a muscle of a person is an actuator and a viscoelastic variable control mechanism. A pneumatic rubber artificial muscle represented by McKibben artificial muscle in artificial muscles has viscoelastic characteristic similar to that of a muscle.
An artificial muscle actuator generates force only in a contracting direction, so that it has to be arranged in an antagonistic manner. A two-joint link model with three pairs of antagonistic muscles has been proposed, in which artificial muscle actuators are arranged so as to be opposite to each other, and bi-articular actuators are arranged so as to be opposite to each other to the first link and the second link (Robot arm constructed with bi-articular muscles, Toru Oshima, Minayori Kumamoto, Transactions of the Japan Society of Mechanical Engineers. C, vol. 61, 1995, pp. 4696-4703 (hereinafter referred to as Non-Patent Document 1)). The bi-articular actuator is an actuator that is arranged in order to simultaneously drive the first link and the second link. The stiffness at a tip of the second link is represented by an ellipse (hereinafter referred to as “stiffness ellipse”) indicating a stiffness characteristic (distribution of stiffness).
In the Non-Patent Document 1, a long axis, a short axis, and a tilt angle of the stiffness ellipse are arbitrarily set. Adjusting the tilt of the stiffness ellipse can realize the stiffness characteristic for allowing the disturbance direction and the moving direction of the hand to agree with each other when external force is applied to the hand. Specifically, the elasticities of the artificial muscle actuators may be made equal to each other under the condition that the lengths of two links are made equal to each other, and the tilt angle may be set such that the long axis or the short axis of the stiffness ellipse is overlapped on a line linking the joint at a base end of the first link and the tip of the second link. Thus, compliance control can be performed only by controlling the elasticities of the artificial muscle actuators.
However, the Non-Patent Document 1 is based on the premise that the lengths of two links are equal to each other. The Non-Patent Document 1 does not describe the method of independently setting the elasticities of the artificial muscle actuators of three pairs of antagonistic muscles in order to realize the optimal stiffness ellipse, in case where the length of two links are different from each other.
Specifically, when the lengths of two links are equal to each other, it is possible to algebraically solve a relational expression between the slight hand displacement and the slight external force with respect to the stiffness of each actuator pair, wherein the relational expression is obtained by introducing Jacobian matrix under the condition that the axis of the stiffness ellipse tilts by the tilt angle φ. Accordingly, even when the lengths of two links are different from each other, it is considered that, as a method of realizing an optimal stiffness ellipse, a relational expression between the slight hand displacement and the slight external force is solved with respect to the stiffness of each actuator pair, wherein the relational expression is obtained by introducing Jacobian matrix under the condition that the axis of the stiffness ellipse tilts by the tilt angle φ.
However, it is difficult to algebraically obtain a solution of the relational expression. Therefore, the real method is to form the optimal stiffness ellipse with a method of performing a convergent calculation. The calculation amount for the convergent calculation is enormous, which means that it takes much time for the convergent calculation. Therefore, the stiffness ellipse cannot be formed with high speed by the convergent calculation. Accordingly, the desired stiffness ellipse cannot rapidly be obtained, whereby the controllability of the stiffness by the actuators is poor.
In view of this, the present invention aims to provide a robot apparatus that can rapidly obtain an ellipse indicating a stiffness characteristic, even if lengths of two links are different from each other.